But
* What would happen if a question was given with larger, unfactorable numbers?
* What would happen if there were decimals in the question?
* What would happen if there seemed to be no "visible" solution?
Luckily, mathematicians have discovered a method that would enable us to find the zeros of any expression.
This method is called The Quadratic Formula.
For proof of this theorem, see page 397 of the text.
Recall, that in Standard Form, the equation of a parabola is as follows:
ax² + bx + c = 0
Therefore, when using the Quadratic Formula, "a" represents the coefficient on the quadratic term (the x² term), "b" represents the coefficient on the linear term (the x term) and "c" represents the constant term (the non-x term).
Example 1 Find the zeros for the following expression: y = 2x² + 3x - 5.
Another useful "tool" within the Quadratic Formula is something called the discriminant.
The discriminant refers to the section b² - 4ac.
* If the discriminant is greater than zero, then the parabola crosses the x-axis twice; there are 2 solutions.
* If the discriminant is equal to zero, then the parabola touches down on the x-axis only once; this is the vertex.
* If the discriminant is less than zero (a negative value), then the parabola never crosses the x-axis; there are no solutions.
Practice Questions
Page 403 #4 odd, 5 odd, 6 (column 1), 11 (column 2), 12
